Combinatorics

Answer a bc by the deni5on of set minus a bc

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: CSCE 235 Combinatorics 10 PIE Theorem: Example 2 •  To illustrate, when n=4, we have |A1∪A2∪A3∪A4|= |A1|+|A2|+|A3|+|A4| - [|A1∩A2|+|A1∩A3|+|A1∩A4| +|A2∩A3|+|A2∩A4|+|A3∩A4|] + [|A1∩A2∩A3|+|A1∩A2∩A4| +|A1∩A3∩A4|+|A2∩A3∩A4|] - |A1 ∩A2 ∩A3 ∩A4| CSCE 235 Combinatorics 11 Applica5on of PIE: Example A (1) •  How many integers between 1 and 300 (inclusive) are –  Divisible by at least one of 3,5,7? –  Divisible by 3 and by 5 but not by 7? –  Divisible by 5 but by neither 3 or 7? •  Let A = {n∈Z | (1 ...
View Full Document

This note was uploaded on 10/31/2013 for the course CSCE 235 taught by Professor Staff during the Spring '08 term at UNL.

Ask a homework question - tutors are online